In this article we will discuss about how to measure discharge of a river or canal used for irrigation.
Measurement of Discharge:
While measuring discharge of a river or canal, one has to measure:
(i) The area of cross-section and
(ii) The average velocity of flow.
If both these elements are known, the discharge flowing through any particular point of the canal or river is found out by multiplying both of them. Before different methods of discharge measurement are discussed, let us discuss the methods of measuring area of cross-section and those for measuring velocity of flow.
Measurement of Area off Cross-Section:
In the case of canals there is no difficulty in measuring the cross-sectional area. Canals are always of some regular shape whose area can be found out by any geometrical formula. But in case of natural streams and rivers, it is not very easy to determine the area of cross-section as their sections are not regular.
In this case area of cross-section of the river can be determined as follows:
See Fig. 10.1. A river is flowing from left to right. Select AB, CD and EF sections of the river and pull cables at all these sections across the river. The distance between sections AB, CD, and CD, EF may be anything, say 100 m.
Wooden battens are attached to all the cables and sections of river at the cable points are divided into equal parts. In our case we have divided each cable into seven equal parts as shown in Fig. 10.2. Thus the river width gets divided into seven equal parts longitudinally.
Now take a staff or any other graduated rod and measure the depth of the river at the centre points of the each of the seven parts. Compute the areas of all seven compartments by multiplying the width of the water of each compartment by the depth of the water at the centre of each corresponding compartment. The sum of all these areas is the cross-sectional area (A) of the flowing water of the river.
If it is not possible to measure the depth of water with staff or graduated rod, it can be measured by using measures like Kelvin’s tube, Echo sounder etc.
Measurement of Velocity of Flow:
Before we actually discuss various methods to measure the velocity of flow, it is worthwhile to explain the variation in the velocity along the cross-section of the river.
The velocity of flow is not uniform throughout the cross-section of the river. It is almost zero at the bed and increases parabolically as we proceed towards the surface of water. But the velocity is maximum slightly below the surface. At surface velocity is somewhat less than the maximum.
Now if we proceed along the width of the river, the velocity is almost zero along the banks. The velocity goes on increasing as we proceed towards the centre of the river and it reaches maximum at the centre.
Now if we consider, both along depth and along the width of the river, we can easily pin point that velocity of flow is maximum at centre width of the river but slightly below the surface of water. The velocity is zero along banks and bed of the river. If we draw contours of equal velocity they will be as shown in Fig. 10.3 (a).
Seeing variation in velocity along depth as well as along width of the river, it can be easily understood that finding the average velocity of flow is not very easy. One has to take average of the velocities along depth as well as width for all the seven compartments of Fig. 10.2.
Methods of Measuring the Average Velocity of Flow:
Following six methods can be used for determining the average velocity of flow:
1. Surface Floats:
A float or surface float is nothing but a piece of cork or anything which can float on water. Such a float gives surface velocity of flow only. The distance travelled by such a float divided by the time taken to travel a specified distance, gives the surface velocity of flow. Surface floats are simultaneously released in each of the seven compartments of the river and time taken by the float of each compartment in reaching section EF from AB is noted.
Surface velocity for each compartment can then be computed by dividing the distance between AB and EF, by the time taken by the float of the corresponding compartment. After having found out the surface velocities, the mean velocities can be calculated for each compartment by multiplying the surface velocities by a suitable coefficient 0.85. Average of all the mean velocities can then be found out, which is overall average velocity (V) of the flow.
2. Double Floats:
It is just like a surface float with the difference that it is attached with a steel ball. The steel ball remains suspended in water. The ball is maintained at such depth that the resulting velocity of the float is not the surface velocity but average velocity. Time of travel of the float is noted for all the compartments dividing width of the river and average of the velocities for all the zones is found out which is considered as average velocity of flow.
3. Velocity Rods:
These are wooden rods painted with some water proofing paint. A weight is attached to the bottom of the rod. The weight is so adjusted that rod length equal to 0.94 x depth remains inside the water. The top about 4 cm length of the rod remains out of water and remains visible. These rods when floated in flowing water give the mean velocity of flow directly.
The use of floats and velocity rods is generally restricted to straight rivers having almost uniform cross-section throughout. They are not of much use for natural stream, especially when depth of water exceeds 1.5 m or so.
4. Current Meter:
It is one of the best methods for measuring the velocity of natural stream. Various types of current meters are in use these days, but the most common and widely used in India is the Price’s current meter.
It is a differential type of meter and consists of a horizontal wheel carrying a series of cups that rotate on a vertical axis. Half of the cups behave convex and half as concave to the current. There is a tail-vane and a counter weight at bottom to balance the meter and to keep it steady.
When current meter is suspended in water, the velocity of flow causes the wheel to rotate. The current meter is fitted with a device so as to record the number of revolutions of the horizontal wheel due to velocity of flow. The rate of revolutions is proportional to the velocity of flow.
Since the velocity for different compartments is different, hence the meter is lowered in the centre of each compartment separately and individually. The wheel of the meter should face the current and is generally kept at a depth of 0.6 depth from the free surface of water. The velocity measured by keeping the meter at a depth of 0.6 depth, gives the mean velocity.
Sometimes the velocities at a depth of 0.2 depth and 0.8 depth are measured and their average value is taken to be the mean velocity. The current meter is used by suspending it with the help of a boat. For narrower streams the meter can be suspended by a cable stretched across the river and at the mid-points of each compartment.
The boat can be conveniently used for small velocities of the order of 1 m/sec but for higher velocities and rough waters, it becomes difficult to keep the boat steady. In such a case the boat is generally anchored.
5. Pitot Tube:
It is a device with the help of which velocity head of flowing water is converted into pressure head. The pressure head can be measured and the velocity of flow calculated by equating their pressure head to V2 / 2g.
Pitot tube is an ordinary tube having both ends open. The bottom end is bent at 90°. It may be having two rods one rod facing the current of water and other against the current. Velocity of flow can be determined by using Bernoullis equation –
6. Travelling Screen Method:
This method cannot be used for rivers or streams. This method can be used for canals and that too for lined canals. The method consists of a canvass screen mounted on a frame work of iron angles. The size of the screen is so adjusted that some open space remains between bottom and banks, and the canvass bottom and edges respectively.
The whole frame work is mounted on a travelling trolley which can move on the rails laid at banks and parallel to the canal. When canvass screen is put against the current of flowing water it starts moving because of thrust of water. The velocity of moving screen is taken as the average velocity of flow. The method is not very common.
Methods of Measuring the Discharge:
Discharges of rivers, streams and canals can be measured by following methods:
1. Area Velocity Method:
This is the direct method of computing the discharge in a stream by measuring its velocity and area of flow. The methods of computing average velocity of flow and also those of area of cross- section of flow. The discharge is nothing but multiplication of the average velocity of flow and that of area of cross-section of water.
2. Weir Method:
Various kinds of weirs are installed across the river streams to measure the discharge. The head of water over the weir crest is measured and the discharge is calculated by using the appropriate formula. Weirs are generally used for measuring discharge of small rivers and canals. For large streams the discharge is generally measured using spillway of dams as weirs.
Following formulae may be used for different types of weirs:
(i) Cippoletti weir
Q = 1.83 LH3/2
(ii) 90° V-Notch
Q = 1.45 H5/2
3. Flumed Meters:
In this method the canal or river is flumed i.e. reduced in section, either by raising the bottom of the channel or by decreasing the width of the channel or by both ways. Let B be the normal width and b the width at the flumed part of the channel.
Let V and v be the velocities of flow at normal section and throat respectively. If there is no head loss between normal section and throat, then total heads at normal section and throat, will be as follows. Let H and h be the depths of water respectively at normal and throat section. See Fig. 10.8.
Total head at normal section = H + V2 / 2g
The length of the throat should be kept small to keep the energy losses minimum.
4. Chemicals Method:
This method is not used much and as such is not important. It is also known as salt titration or salt solution method.
5. Stage Discharge Curve:
It is a curve which tells us the relation between the discharge and the depth of water. In this case several observations at different gauge heights are taken and corresponding discharges computed. Discharges and corresponding gauge heights are plotted. The curve so obtained is known as station rating curve or discharge curve.
After such a curve has been drawn, it is very easy to find out discharge simply by reading the gauge and finding out the corresponding discharge from such a curve. A typical stage discharge or station rating curve is shown in Fig. 10.9.
This curve gives us a relationship between the stage of the river at a given time (gauge height) and the corresponding discharge. Hence it is also known as stage discharge curve. The relation expressed by this curve is known as stage discharge relationship.
If river bed has changed due to silting or scouring the same stage discharge curve will not hold good. The stage of a river may be constant, left rising or falling. During the rising stage, the measured discharge is more than that for a constant stage. Similarly during a falling stage, the measured discharge will be less than that for a constant stage.
6. From Power Plant Records:
This method is an indirect method of computing discharge of the river. It is most accurate method and is generally adopted at places where no direct method such as weir station, or other measuring station is available.
Power plants are generally installed on the rivers and their operating records help us in determining the mean daily discharge passed through those plants. The total flow passing through a power plant is the summation of –
(i) Flow through turbines
(ii) Flow over spillways
(iii) Flow through various sluices and leakages.
The quantities of all these flows can be computed separately and totaled to obtain the total discharge of the river. This method is especially used during flood peaks as it gives the most accurate result.
Measurement of Discharge by Area Velocity Method for Big Rivers:
The cables may be stretched across the river and river width divided into small compartments by fixing tags to the cable. But in case of very large and wide rivers it is not possible to stretch cables across the river. In that case pivot method is used. It consists of a long high pole installed at one bank of the river.
A long wooden plank is fixed to this pole at some height. The plank consists of a number of equidistant holes. P is the point of observation. The last hole B, on the plank is made in such a way that the observer from point P when views through hole B7 strikes point B7 at the opposite bank of the river. B7 is the last point where river water at H.F.L. is touching the opposite bank. See Fig. 10.10.
Now by observing from P through points Bv1, B2, B3………….. B7, corresponding points A1, A2, A3 in the river can be fixed. The velocity of flow for each compartment is then found out with the help of a current meter. Depths of water at the centre of each compartment are found out by going in boat. The discharge of the river is finally found out by adding together the discharges flowing in all the compartments separately.